## Osaka Journal of Mathematics

### Twisted cohomology for hyperbolic three manifolds

#### Abstract

For a complete hyperbolic three manifold $M$, we consider the representations of $\pi_{1}(M)$ obtained by composing a lift of the holonomy with complex finite dimensional representations of $\mathrm{SL}(2,\mathbf{C})$. We prove a vanishing result for the cohomology of $M$ with coefficients twisted by these representations, using techniques of Matsushima--Murakami. We give some applications to local rigidity.

#### Article information

Source
Osaka J. Math., Volume 49, Number 3 (2012), 741-769.

Dates
First available in Project Euclid: 15 October 2012

https://projecteuclid.org/euclid.ojm/1350306595

Mathematical Reviews number (MathSciNet)
MR2993065

Zentralblatt MATH identifier
1255.57018

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20C15: Ordinary representations and characters

#### Citation

Menal-Ferrer, Pere; Porti, Joan. Twisted cohomology for hyperbolic three manifolds. Osaka J. Math. 49 (2012), no. 3, 741--769. https://projecteuclid.org/euclid.ojm/1350306595

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